(a) How much charge does a battery have to supply to a 5.0 uF capacitor to create a potential difference of 1.5 V across its plates? How much energy is stored in the capacitor in this case? (b) How much charge would the batter have to supply to store 1.0 J of energy in the capacitor? What would be the potential across the capacitor in this case.
Once again, I am lost!!!
a) C = q/V so q = C V
= 5*10^-6 * 1.5
= 7.5 * 10^-6 Coulombs
now do E = (1/2) C (1.5)^2 to get energy
E = .5 (5*10^-6)(2.25)
E = 5.63*10^-6 Joules
b) Luckily we derived this in your last question, but now that I see your questions you probably have it in your book and have not had calculus so
E = (1/2) C V^2 from your book or the other problem
E = (1/2) C (q/C)^2
(q/C)^2 = 2 E/C
q^2/C^2 = 2 E/C
q^2 = 2 E C
q = sqrt (2E*C)
q = sqrt (2 * 5 * 10*-6)
q = 10^-3 sqrt (10)
q = 3.16 * 10^-3 coulombs
c)V = q/C = 2.24*10^-3 / 5*10^-6
V = .447* 10^3 = 447 volts, watch out
Good but quite difficult to understand.
(a) Well, the charge needed can be found by using the formula Q = CV, where Q is the charge, C is the capacitance, and V is the potential difference. So, plug in the values: Q = (5.0 uF) * (1.5 V). Now I need to convert that pesky microfarad to farad. Let's see... if a regular farad was a person, a microfarad would be like an ant on Thanksgiving dinner. So we'll need to divide by a million to make it a regular farad. That gives us Q = (5.0 * 10^(-6) F) * (1.5 V). And when you do the math, you'll find that the charge needed is a teeny tiny value.
Now, to calculate the energy stored in the capacitor, we use the formula E = 0.5 * CV². So plug in the values again: E = 0.5 * (5.0 * 10^(-6) F) * (1.5 V)². And when you multiply it all out, you get the energy stored in the capacitor.
(b) To store 1.0 J of energy in the capacitor, we'll need to find the charge again using the formula E = 0.5 * CV². So, rearrange the formula a bit to get Q = √(2E/C), where Q is the charge, E is the energy, and C is the capacitance. Plug in the values: Q = √(2 * 1.0 J) / (5.0 * 10^(-6) F). Do the math, and you'll find the charge required.
As for the potential across the capacitor, it can be found by using the formula V = Q/C. Plug in the values one more time: V = (charge obtained before) / (5.0 * 10^(-6) F). And voilà, you have the potential difference across the capacitor!
I hope that helps you find your way through the capacitor labyrinth!
No problem, I'm here to help! Let's break down the questions step-by-step.
(a) To find the charge supplied by the battery, we can use the formula:
Q = C * V
Where:
Q is the charge
C is the capacitance of the capacitor
V is the potential difference across the plates
Given:
C = 5.0 uF = 5.0 * 10^(-6) F
V = 1.5 V
We can substitute these values into the formula:
Q = (5.0 * 10^(-6)) F * 1.5 V
Calculating this, we get:
Q = 7.5 * 10^(-6) Coulombs
So, the battery needs to supply 7.5 * 10^(-6) Coulombs of charge to the capacitor.
To find the energy stored in the capacitor, we can use the formula:
E = 0.5 * C * V^2
Where:
E is the energy stored in the capacitor
Again, substituting the given values:
E = 0.5 * (5.0 * 10^(-6)) F * (1.5 V)^2
Calculating this, we get:
E = 5.625 * 10^(-6) Joules
Therefore, the capacitor would store 5.625 * 10^(-6) Joules of energy in this case.
(b) To find the charge required to store 1.0 J of energy in the capacitor, we can rearrange the formula for energy:
E = 0.5 * C * V^2
And solve for charge:
Q = sqrt((2 * E) / C)
Given:
E = 1.0 J
C = 5.0 * 10^(-6) F
Substituting the values:
Q = sqrt((2 * 1.0 J) / (5.0 * 10^(-6) F))
Calculating this, we get:
Q ≈ 6.32 * 10^(-3) Coulombs
Therefore, the battery would have to supply approximately 6.32 * 10^(-3) Coulombs of charge to store 1.0 J of energy in the capacitor.
To find the potential across the capacitor, we can rearrange the formula for charge:
Q = C * V
And solve for potential:
V = Q / C
Substituting the values:
V = (6.32 * 10^(-3) Coulombs) / (5.0 * 10^(-6) F)
Calculating this, we get:
V ≈ 1,264 Volts
Therefore, the potential across the capacitor would be approximately 1,264 Volts in this case.
No problem, let me guide you through the steps to solve these questions.
(a) To find the charge that the battery needs to supply to the capacitor, we can use the formula for capacitance:
C = Q/V,
where C is the capacitance, Q is the charge, and V is the potential difference across the capacitor. Rearranging this equation, we have:
Q = C * V.
Plugging in the given values: C = 5.0 uF = 5.0 * 10^(-6) F and V = 1.5 V, we can calculate:
Q = (5.0 * 10^(-6) F) * (1.5 V).
By multiplying these numbers, you will get the charge (in coulombs) that the battery has to supply to the capacitor.
To find the energy stored in the capacitor, we can use the equation:
E = (1/2) * C * V^2,
where E is the energy stored in the capacitor.
Plugging in the given values: C = 5.0 uF = 5.0 * 10^(-6) F and V = 1.5 V, we can calculate:
E = (1/2) * (5.0 * 10^(-6) F) * (1.5 V)^2.
By simplifying and calculating, you will get the energy stored in the capacitor (in joules).
(b) To find the charge that the battery needs to supply to store 1.0 J of energy in the capacitor, we can rearrange the energy equation as follows:
E = (1/2) * C * V^2,
to solve for Q:
Q = 2 * E / V.
Plugging in the given values: E = 1.0 J and V is unknown, we can calculate:
Q = 2 * (1.0 J) / V.
This will give you the charge (in coulombs) that the battery has to supply to the capacitor.
To find the potential difference across the capacitor in this case, we can rearrange the energy equation as follows:
E = (1/2) * C * V^2,
to solve for V:
V = sqrt(2 * E / C).
Plugging in the given values: E = 1.0 J and C = 5.0 uF = 5.0 * 10^(-6) F, we can calculate:
V = sqrt(2 * (1.0 J) / (5.0 * 10^(-6) F)).
By simplifying and calculating, you will get the potential difference across the capacitor (in volts).